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Langmuir 2007, 23, 7078-7082
Calibration of Friction Force Signals in Atomic Force Microscopy in Liquid Media Ewa Tocha, Jing Song, Holger Scho¨nherr,* and G. Julius Vancso* Department of Materials Science and Technology of Polymers, MESA+ Institute for Nanotechnology and Faculty of Science and Technology, UniVersity of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands ReceiVed January 20, 2007. In Final Form: April 4, 2007 The calibration factors for atomic force microscopy (AFM) friction force measurements in liquid media are shown to be different by 25-74% compared to measurements in air. Even though it is significantly more precise, the improved wedge calibration method using a universal calibration specimen suffers, as all other widely applied methods, from the drawback that friction force calibration factors acquired in air cannot be used for measurements in liquids for the most common liquid cell designs. The effect of laser light refraction and the dependence of the calibration factors on the refractive index of the imaging medium is captured quantitatively in a simple model that allows one to conveniently rescale the values of lateral photodiode sensitivity obtained in air. Hence a simple, yet precise calibration of lateral forces is now also feasible for AFM in liquids.
Introduction The development of atomic force microscopy (AFM) has provided access to the observation of the details of (supra)molecular structures and to the determination of intermolecular forces with high force and spatial resolution.1-4 Among the different modes of AFM, measurements of lateral (friction) forces have taken up a central role both in fundamental studies of (nano)tribology5-12 and in the compositional mapping of patterned or multiphase thin organized film assemblies and so forth.13-15 The quantitatiVe determination of nanotribological properties in liquid environment is also essential for understanding, among other things, various biological systems, as well as several applications such as MEMS valves, micropumps, and micromotors.16-18 * Corresponding authors. E-mail:
[email protected]; tel.: ++31 53 489 3170; fax: ++31 53 489 3823 (H.S.). E-mail: g.j.vancso@ tnw.utwente.nl; tel.: ++31 53 489 2967; fax: ++31 53 489 3823 (G.J.V.). (1) Butt, H. J.; Cappella, B.; Kappl, M. Surf. Sci. Rep. 2005, 59, 1. (2) Carrion-Vazquez, M.; Oberhauser, A. F.; Fisher, T. E.; Marszalek, P. E.; Li, H. B.; Fernandez, J. M. Prog. Biophys. Mol. Biol. 2000, 74, 63. (3) Hansma, H. G.; Kim, K. J.; Laney, D. E.; Garcia, R. A.; Argaman, M.; Allen, M. J.; Parsons, S. M. J. Struct. Biol. 1997, 119, 99. (4) Vancso, G. J.; Hillborg, H.; Scho¨nherr, H. In AdVances in Polymer Science; Springer: Berlin, 2005; Vol. 182, p 55. (5) Carpick, R. W.; Salmeron, M. Chem. ReV. 1997, 97, 1163. (6) Bhushan, B. Handbook of Micro/Nano Tribology; CRC Press: New York, 1999. (7) Schwarz, U. D.; Allers, W.; Gensterblum, G.; Wiesendanger, R. Phys. ReV. B 1995, 52, 14976. (8) Enachescu, M.; van den Oetelaar, R. J. A.; Carpick, R. W.; Ogletree, D. F.; Flipse, C. F. J.; Salmeron, M. Phys. ReV. Lett. 1998, 81, 1877. (9) Mate, C. M.; McClelland, G. M.; Erlandsson, R.; Chiang, S. Phys. ReV. Lett. 1987, 59, 1942. (10) Liley, M.; Gourdon, D.; Stamou, D.; Meseth, U.; Fischer, T. M.; Lautz, C.; Stahlberg, H.; Vogel, H.; Burnham, N. A.; Duschl, C. Science 1998, 280, 273. (11) Gnecco, E.; Bennewitz, R.; Gyalog, T.; Loppacher, C.; Bammerlin, M.; Meyer, E.; Gu¨ntherodt, H. J. Phys. ReV. Lett. 2000, 84, 1172. (12) Hurley, C. R.; Leggett, G. J. Langmuir 2006, 22, 4179. (13) Frisbie, C. D.; Rozsnyai, L. F.; Noy, A.; Wrighton, M. S.; Lieber, C. M. Science 1994, 265, 2071. (14) Sun, S.; Leggett, G. J. Nano Lett. 2004, 4, 1381. (15) For recent reviews, see ref 4 and Scho¨nherr, H.; Vancso, G. J. In Scanning Probe Microscopies Beyond Imaging: Manipulation of Molecules and Nanostructures; Samori, P., Ed.; Wiley-VCH: Weinheim, Germany, 2006; p 275. (16) Zhang, W. M.; Meng, G. A. Microsyst. Technol. 2006, 12, 283. (17) Wang, C. H.; Lee, G. B. Biosens. Bioelectron. 2005, 21, 419. (18) Zhang, W. M.; Meng, G.; Li, H. G. Microelectron. Reliab. 2005, 45, 1230.
Despite its obvious importance, the reliable calibration of friction forces in AFM remained, until recently, a difficult task. The frequently applied two-step calibration methods19-21 based on the determination of the cantilever lateral spring constant kL and the lateral photodiode sensitivity SL may be highly inaccurate, as shown recently,22 due to poorly defined cantilever material properties, the imprecise determination of the cantilever thickness, and the inaccuracy in estimating SL. These limitations are overcome in the direct calibration procedure called the wedge calibration method, which was introduced by Ogletree et al.23 and further improved by Varenberg et al.24 In this method, the friction signal is recorded as a function of the applied load on a calibration sample with two well-defined slopes. The friction force calibration factor is determined from the lateral force relations measured on differently sloped surfaces, thus enabling one to convert the experimentally obtained photodiode response in volts, as a measure of the torsion moment, into the corresponding friction force in newtons. The calibration of all types of probe cantilevers, independent of cantilever geometry and tip radius, can be performed with an error of only ca. 5% using the universal calibration specimen recently introduced by our group.22 Despite this success, the improved wedge calibration method suffers, similar to the reference techniques, the two-step and direct procedures, from the fact that calibration factors obtained in ambient air or defined gas atmospheres cannot be a priori utilized in AFM experiments carried out in liquid media for most commercial AFM instruments. As considered here explicitly for the first time, in such cases, refraction of the laser light (used in the beam deflection detection) leads to systematic errors. Due to the importance of friction forces in liquid cell AFM, for example, in chemical force microscopy (CFM),4,25,26 in studies (19) Liu, E.; Blanpain, B.; Celis, J. P. Wear 1996, 192, 141. (20) Noy, A.; Frisbie, C. D.; Rozsnyai, L. F.; Wrighton, M. S.; Lieber, C. M. J. Am. Chem. Soc. 1995, 117, 7943. (21) Schwarz, U. D.; Ko¨ster, P.; Wiesendanger, R. ReV. Sci. Instrum. 1996, 67, 2560. (22) Tocha, E.; Scho¨nherr, H.; Vancso, G. J. Langmuir 2006, 22, 2340. (23) Ogletree, D. F.; Carpick, R. W.; Salmeron, M. ReV. Sci. Instrum. 1996, 67, 3298. (24) Varenberg, M.; Etsion, I.; Halperin, G. ReV. Sci. Instrum. 2003, 74, 3362. (25) Vezenov, D. V.; Noy, A.; Ashby, P. J. Adhes. Sci. Technol. 2005, 19, 313.
10.1021/la070174v CCC: $37.00 © 2007 American Chemical Society Published on Web 05/26/2007
Calibration of AFM Friction Force in Liquid Media
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Figure 1. Simplified side-view schematic (not to scale) of an AFM experiment carried out using a liquid cell. The light paths for two cantilever deflections are indicated for media with different refractive indices (normal bending signals: black line, light path in liquid; red line, light path in air). We denote the cantilever bending angle as θ and the angle between cantilever and holder as γ ) 1/2R. n, nair and R, β stand for the refractive indices of the liquid and air, and the entry/exit angles for light propagating through the liquid-quartz and quartz-air interfaces, respectively.
of phenomena and structures intrinsic to solid-liquid interfaces27-31 and for in situ studies of biological processes,32-34 there is a clear need to address this shortcoming. As shown in this paper, the altered laser light path, as a result of refraction, can be accounted for using a simple model and a correction factor that relates the photodiode response for measurements in air and in a given liquid (with a given refractive index). This correction can be applied for all three classes of calibration procedures and all commonly used cantilever geometries. Thus, the systematic error described can be conveniently eliminated. Experimental Section Materials. Ethanol (purity g99.9%) and iodomethane (purity g99%) were purchased from Merck, and diiodomethane (purity >99%) was obtained from Aldrich. Bare Si (100) wafers with a native oxide layer were cleaned prior to the measurements by being rinsed thoroughly with chloroform and ethanol. High-purity and deionized water (18.2 MΩ cm) was used from a Milli-Q system. AFM and Calibration Procedure. Photodiode sensitivities for vertical (surface-normal) deflection, termed normal photodiode sensitivities, SN, were determined in air, and the different liquids (water, ethanol, iodomethane, and diiodomethane) were determined in a quartz liquid cell using a NanoScope III (Digital Instruments/ (26) Noy, A.; Vezenov, D. V.; Lieber, C. M. Annu. ReV. Mater. Sci. 1997, 27, 381. (27) Marti, A.; Ha¨hner, G.; Spencer, N. D. Langmuir 1995, 11, 4632. (28) Ha¨hner, G.; Marti, A.; Spencer, N. D. Tribol. Lett. 1997, 3, 359. (29) Scho¨nherr, H.; Johnson, J. M.; Lenz, P.; Frank, C. W.; Boxer, S. G. Langmuir 2004, 20, 11600. (30) Holmberg, M.; Kuhle, A.; Garnaes, J.; Morch, K. A.; Boisen, A. Langmuir 2003, 19, 10510. (31) Reviakine, I.; Brisson, A. Langmuir 2000, 16, 1806. (32) Mu¨ller, M.; Lee, S.; Spikes, H. A.; Spencer, N. D. Tribol. Lett. 2003, 15, 395. (33) Pasche, S.; De Paul, S. M.; Voros, J.; Spencer, N. D.; Textor, M. Langmuir 2003, 19, 9216. (34) Mu¨ller, M. T.; Yan, X. P.; Lee, S. W.; Perry, S. S.; Spencer, N. D. Macromolecules 2005, 38, 3861.
Veeco, Santa Barbara, CA) atomic force microscope. Forcedisplacements (f-d) curves were acquired for the different media using a V-shaped silicon nitride cantilever (Model NP, Veeco Nano Probe, Santa Barbara, CA) with a normal spring constant of 0.12 N/m (ref 35), and, alternatively, a single-beam silicon nitride cantilever (model OMCL-RC800PSA, Olympus, Tokyo, Japan, coated on the tip side with 15 nm Ti) with a normal spring constant of 0.12 N/m on a precleaned (100) Si substrate with a native oxide layer, without changing the laser light position on the cantilever apex for the corresponding series of experiments (f-d curve acquisition parameters: z ramp size, 500 nm; frequency, 1 Hz). The liquids (10 mL) were exchanged in the order water-ethanol-(di)iodomethane, and measurements were carried out after at least 20 min of equilibration time after liquid exchange. Independent measurements after the liquid-cell was thoroughly dried and refilled with a given liquid resulted in identical results to within the errors stated. SN was readily obtained by estimating the slope of the linear compliance region, where the tip and the sample are in hard wall contact. The typical distributions of SN obtained are shown in the Supporting Information. We report data from three independent experiments with three individual cantilevers. The mirror rotation angle φ was determined from digital photographs (Konica-Minolta Dynax 7D, Tokyo, Japan) of the optical head after adjusting the mirror position for air and the different liquids.
Results and Discussion The direct application of the friction force calibration factor (or SL) determined in air for the friction force calibration of the experimental data obtained in liquids results in an overestimation of the friction forces. The path of the laser beam from the cantilever apex to the photodiode for experiments in liquid is different compared to the situation in air due to refraction caused by the different refractive indices of the different media traversed by the light (Figure 1). Consequently, this will change the photodiode response to the bending and twist angles of the cantilever that (35) Butt, H. J.; Jaschke, M. Nanotechnology 1995, 6, 1.
7080 Langmuir, Vol. 23, No. 13, 2007
Tocha et al. Table 1. Comparison of Laser Path Length for Air and Liquid Measurements, Calculated for Media with Different Refractive Indicesa
air water ethanol iodomethane diiodomethane
n
φ
AA4 [mm]
1.00 1.36 1.34 1.53 1.74
37 31 31 28 25
31.4
AA*4L [mm] 31.8 31.8 31.8 31.8
a Calculated with the following values: K ) 20 mm, M ) 10 mm, L ) 8.5 mm, and R ) 16°.
Figure 2. Schematic (approximately to scale) of an AFM experiment carried out using a liquid cell. The light paths for normal cantilever deflection are indicated for media with different refractive indices. n, nair and R, β denote the refractive indices of the liquid and air, and the entry/exit angles for light propagating through the liquidquartz and quartz-air interfaces, respectively. We denote the mirror rotation angle as φ, the vertical distance between the cantilever apex and the mirror rotation axis as K, the horizontal distance between the photodiode and the mirror rotation axis as M, the horizontal distance between the incident beam and the mirror rotation axis as L, and the angle between the cantilever and the holder as γ ) 1/2R. x and h stand for the horizontal and vertical distances of the reflected laser beam on the mirror relative to the rotation axis, respectively.
correspond to the movement of the laser spot on the photodiode in the vertical and horizontal directions, respectively. In conventional contact-mode AFM height imaging and forcevolume data acquisition, this effect can be corrected on not too soft samples in situ by determining the photodiode sensitivity SN in f-d curves. SN is obtained by estimating the slope of the linear compliance region, where the tip and the sample are in hard wall contact. However, for lateral force microscopy (LFM), the corresponding sensitivity SL cannot be easily obtained in situ. The only precise and reliable calibration methods available have not been used in liquid, even though there are no fundamental reasons not to use them in conjunction with a liquid cell. Hence the setup is calibrated in air, and the calibration factors obtained are used for the liquid cell experiments. As shown below, depending on the liquid medium (refractive indices may range from 1.25 to 1.74 for perfluorohexane and diiodomethane, respectively; water has a refractive index of 1.36),36 the determined friction coefficients are overestimated by a systematic error in the range of 25-74% (36% for water). Determination of the Correction Factor. The correction of the refraction effect mentioned above can be derived based on an analysis of the altered laser light path. The optical paths of laser light reflected off the cantilever as a means to determine the vertical deflection of the cantilever are schematically shown in Figure 1 for measurements in air and in a liquid. In most of the commercial AFM setups, the laser beam enters the liquid cell approximately vertically (at an angle of ∼90° with respect to the liquid cell surface) and will thus not be influenced by different (36) Lide, D. R. CRC Handbook of Chemistry and Physics, 87th ed.; CRC Press: Boca Raton, FL, 2006/2007.
refractive indices of the different media. The path of the reflected beam, however, is affected by the refractive index of the different media. We denote the path traveled by the light before and after bending the cantilever by an angle θ with AA1A2A3A4 and BB1B2B3B4, respectively; the situation in which the light traverses the liquid-filled cell we denote with a superscript L (compare Figure 1). The lateral shifts of the optical paths due to refraction at the medium-quartz and quartz-air surfaces for air and in liquid are small and can hence be faithfully neglected. For a comparison, the thickness of the liquid cell is ∼6.5 mm compared to the typical length of the optical path of 32.0 mm. The normal photodiode sensitivity SN in nanometers per volt is inversely proportional to the distance between the two laser light reflections on the photodiode in air, A4B4, which can be expressed as a function of the cantilever bending angle θ:
A4B4 ) 2θ (AA1 + A1A2 + A2A3 + A3A4) ) 2θAA4 (1) In addition, we can approximate the distance between the two reflected paths in liquid A4LB4L using the following relation:
A4LB4L ) 2θL (AA1 + A1A2L + A2LA3L + A3LA4L) ) 2θLAA4L (2) The different refractive indices of air and the liquid medium will result in refraction, as indicated in Figure 1. Instead of leaving the liquid cell under an angle R + 2θ, the light leaves under an increased angle β + 2θL. This effect can be described using Snell’s law, as shown in eq 3:
nair sin R sin(R + 2θ) ) ) n sin β sin(β + 2θL)
(3)
where n, nair and R, β denote the refractive indices of the liquid and air, and the entry/exit angles for light propagating through the liquid-quartz and quartz-air interfaces, respectively. As mentioned above, the refraction due to the quartz cell can be faithfully neglected because of the very short path length. Different mirror positions that are required to reflect the light toward the photodiode result in equal lengths of the laser path for measurements in air and in liquid:
AA4 = AA4L
(4)
This equality is quantitatively captured in the simple model shown in Figure 2. The corresponding optical path of the laser light for normal bending of the cantilever in air and in liquids is sketched in Figure 2 approximately to scale. The precise path length AA4 and AA*4L can be determined from dimensions of the optical head as a function of the mirror rotation angle φ. The superscript asterisk (*) indicates the
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Figure 3. Simplified schematic (not to scale) of an AFM experiment carried out using a liquid cell. The light paths for cantilever deflection are indicated for media with different refractive indices (lateral torsion signals: black line, light path in liquid; red line, light path in air). The cantilever torsion angle is denoted as ω.
laser path after adjusting the mirror. Further, we denote the vertical distance between the cantilever apex and the mirror rotation axis as K, the horizontal distance between the photodiode and the mirror rotation axis as M, the horizontal distance between the incident beam and the mirror rotation axis as L, and the angle between the cantilever and the holder as γ ) 1/2R. The horizontal and vertical distance of a reflected laser beam on the mirror relative to the rotation axis x can be approximated in air and in liquid, respectively, as
x = L - KtgR
(5)
h(φ) = xtgφ ) (L - KtgR)tgφ
(6)
and
Similarly, we can write
xL = L - Ktgβ
(7)
hL(φ) = xtgφ ) (L - Ktgβ)tgφ
(8)
and
where β is determined by eq 3. Since the length of AA2 = AA2L is significantly smaller than A2LA4L, and since β can be obtained from eq 3, we can describe the path length in air and in liquid as
From eqs 1-3, the relative change of the vertical photodiode response (A4LB4L/A4B4) between liquid and air can be derived:
A4LB4L SN n ) L) A4B4 nair S N
cos R
(11)
x ( )
n 2 2 1sin R nair
where R is twice the value of the constant inclination angle γ between the cantilever and the cantilever holder. The optical paths of laser light reflected off the cantilever as a means to determine the lateral deflection of the cantilever are schematically shown in Figure 3 for measurements in air and in a liquid. The lateral photodiode sensitivities SL and SLL expressed in nanometers per volt are inversely proportional to the distance between the corresponding laser light reflections on the photodiode in air, a4b4, and in liquid, a4Lb4L, which can be described as a function of the cantilever torsion angle ω and the angle of the refracted beam ωL, respectively:
a4b4 ) 2ω (aa1 + a1a2 + a2a3 + a3a4) ) 2ωaa4
(12)
a4Lb4L ) 2ωL (aa1 + a1a2L + a2La3L + a3La4L) ) 2ωLaa4L (13)
AA4(φ) )
K-h M+x + cos R sin (R + 2φ)
(9)
where the exit angle ωL for liquid measurements is described in eq 14:
AA*L 4 (φ) )
K - hL M + xL + cos β sin(β + 2φ)
(10)
nair sin 2ω ω ) L ) L n sin 2ω ω
The determined path lengths in air and liquid are identical to within an error of 1%, which is negligible (Table 1).
(14)
Since the lengths of the laser light paths for both normal and lateral signals are identical, as reported recently19,22 and as can
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be seen in eq 4, we can approximate equal lengths of the laser path for measurements in air and in liquid:
AA4 ) aa4 ) aa4L ) bb4 ) bb4L
(15)
Consequently, the relative change of the lateral photodiode response between liquid and air (a4Lb4L/a4b4) is equal to the relative changes of the refractive indexes of different media:
a4L b4L SL n ) L) a4b4 n S air
(16)
L
Thus, calibration factors determined in air22 can be converted to the correct calibration factors for liquid by multiplication with nair/nliquid. Experimental Verification. The factors, according to eq 11, to be employed to correct for refraction in media with different refractive indices were confirmed in measurements in air, ethanol, iodomethane, and diiodomethane. These media possess significantly different refractive indexes (nair ) 1.00; nethanol ) 1.34; nwater ) 1.36; niodomethane ) 1.53; ndiiodomethane ) 1.74).36 The experiments were carried out using two different AFM cantilever geometries (V-shaped and single-beam, respectively) in a closed AFM liquid cell. The normal sensitivity deflection sensitivities were determined from f-d curves recorded in air and subsequently in the corresponding liquid (the typical distributions of SN obtained are summarized in the Supporting Information). The mirror position was adjusted for each liquid in order to reflect the laser beam to the center of the photodiode and to keep the path length constant (see above). As shown in Table 2, we observed ratios of measured SN/SNL that agree to within the experimental error with the values calculated according to our simple model, independent of the cantilever geometry, as expected. A cross-correlation shows R2 values for linear fits and forced error-weighted linear fits of 0.99987. This model does not take the possible minor vertical deflection of the cantilever by stress induced by (i) temperature Table 2. Ratios of Normal Photodiode Sensitivities between Air and Different Liquids medium
refractive index
SN/SNL model
SN/SNL experiment
water ethanol iodomethane diiodomethane
V-shaped cantilever 1.36 1.41 1.34 1.39 1.53 1.62 1.74 1.91
1.36 ( 0.07 1.34 ( 0.07 1.56 ( 0.08 1.82 ( 0.09
water ethanol diiodomethane
single-beam cantilever 1.36 1.41 1.34 1.39 1.74 1.91
1.42 ( 0.07 1.47 ( 0.07 1.73 ( 0.09
changes or (ii) different interfacial tensions on the upper (Aucoated) and lower (Si3N4-terminated or Ti-coated for V-shaped and single-beam cantilevers, respectively) side of the cantilever into account. Assuming the same deflection angle θ and torsion angle ω, SN and SL can be directly related for measurements in air (see ref 22). However, SNL and SLL are not similarly related due to the fact that the laser beam is not refracted in the lateral direction in the case of the absence of cantilever torsion, as it is refracted for zero θ vertical deflection. In the former case, eq 16 describes the relation between SL and SLL. The abovementioned additional cantilever deflection in the vertical direction does not affect the lateral sensitivities SL and SLL. Consequently, if we substitute R in eq 11 with zero (as is the case for the lateral deflection in the absence of cantilever torsion), we obtain for SN/SNL a similar dependence as for SL/SLL in eq 16. The excellent agreement of the measured ratios SN/SNL and the calculated ones (based on tabulated refractive indices) shows that our models correctly relate vertical, and hence also lateral, photodiode responses between air and liquid. Thereby, eq 16 enables one to utilize rescaled friction force calibration factors determined in air22 for AFM experiments carried out in liquid. In addition, the slight offset of the constant force set point in conventional contact-mode height imaging in media with different refractive indices, in the case where SN has not been calibrated in situ, can be accounted for by a similar rescaling procedure.
Conclusion The hitherto overlooked effect of laser light refraction for friction force AFM measurements in liquid media and the dependence of the calibration factors on the refractive index of the imaging medium are quantitatively described in a simple model derived in this paper. By multiplication with the factor nair/nliquid, one can conveniently rescale the values of lateral photodiode sensitivity obtained in air (SL) employing, for example, the improved wedge calibration method using a universal calibration specimen to obtain the correct value for SLL. Hence, a simple, yet precise calibration of lateral forces is now also feasible for AFM in liquids. Acknowledgment. This work has been financially supported by the Dutch Polymer Institute (DPI), the Dutch Technology Foundation STW (STW-Project TMF.7424), the MESA+ Institute for Nanotechnology of the University of Twente, and the Council for Chemical Sciences of the Netherlands Organization for Scientific Research (CW-NWO) in the framework of the Vernieuwingsimpuls program (grant awarded to H.S.). Supporting Information Available: Plot of SN(model) vs SN(experiment) and distributions of SN for various media. This material is available free of charge via the Internet at http://pubs.acs.org. LA070174V
